Thanks Ian, you convinced me that the so-called original rivets were not the way to go.
I tried to close a couple up and it was not a nice experience.
With a lot less effort than I expected I reprofiled the heads of some rivets we keep in stock.
The only real pain was that they were about an 1/8" too long.
Below the pictures of the shaft and rivets in place.
I used a course polishing mop to debur the heads.
Followed by an ultra-sonic bath.